Geodesic
Free filtrations of affine Weyl arrangements and the ideal-Shi arrangements
Journal of Algebraic Combinatorics, Tome 43 (2016) no. 1, pp. 33-44.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

In this article, we prove that the ideal-Shi arrangements are free central arrangements of hyperplanes satisfying the dual partition formula. Then, it immediately follows that there exists a saturated free filtration of the cone of any affine Weyl arrangement such that each subarrangement of the filtration satisfies the dual partition formula. This generalizes the main result in Abe et al. (J. Eur. Math. Soc., to appear) which affirmatively settled a conjecture by Sommers and Tymoczko (Trans. Am. Math. Soc. 358:3493-3509, 2006).
Classification : 32S22
Keywords: hyperplane arrangements 
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     author = {Abe, Takuro and Terao, Hiroaki},
     title = {Free filtrations of affine {Weyl} arrangements and the {ideal-Shi} arrangements},
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Abe, Takuro; Terao, Hiroaki. Free filtrations of affine Weyl arrangements and the ideal-Shi arrangements. Journal of Algebraic Combinatorics, Tome 43 (2016) no. 1, pp. 33-44. http://geodesic.mathdoc.fr/item/JAC_2016__43_1_a9/